Worst-case search in constrained uncertainty space for robust H-infinity synthesis

Abstract

Standard H-infinity/H2 robust control and analysis tools operate on uncertain parameters assumed to vary independently within prescribed bounds. This paper extends their capabilities in the presence of constraints coupling these parameters and restricting the parametric space. Focusing on the worst-case search, we demonstrate -- based on the theory of upper-C1 functions -- the validity of standard, readily available smooth optimization to address this nonsmooth constrained optimization problem. Specifically, we prove that for such functions, any subgradient satisfy Karush-Kuhn-Tucker (KKT) conditions at a local minimum, and that any accumulation point of the sequential quadratic programming (SQP) is a KKT point. From a practical point of view, we combine this local exploitation with a global exploration using Monte-Carlo sampling. This worst-case search then enables robust controller synthesis: identified worst-case configurations are iteratively added to an active set on which a non-smooth multi-models optimization of the controller is performed. The proposed approach is illustrated through the robust control of a mechanical system. We show that this method enables fast detection of rare worst-case configurations, and that the robust controller optimization converges with a limited number of active configurations.